Step 1 - Networking
Make sure you have public IP address from your internet provider. Then, forward some UDP port to your computer on your router. The default Crysis server port is 64087.
Step 2 - The first server
In-game server created in Multiplayer -> Internet Game -> Create Game should now be visible in the server list. If it's gray and not visible on the website, then it's not reachable from the internet, meaning nobody can connect. In that case, go back to the first step.
Step 3 - Server modding
https://crymp.org/thread?id=347